Pollard, John M.  
   Factoring, discrete logarithms. Originator of the p-1, lambda, rho and kangaroo methods.
   http://members.lycos.co.uk/John_M_Pollard/

Peneva, Temenoujka  
   University of Plovdiv "Paisii Hilendarski". Analytic number theory: additive prime number theory, distribution of primes, exponential sums, sieve methods, Riemann zeta-function and Dirichlet L-functions.
   http://geocities.com/tpeneva

Pierce, Lillian  
   University of Oxford. Analytic number theory.
   http://www.maths.ox.ac.uk/~piercel/

Pries, Rachel  
   Columbia University. Arithmetic geometry, specifically Galois theory of curves in characteristic p.
   http://www.math.columbia.edu/~pries/

Papanikolas, Matt  
   Texas A+M University. Number theory and arithmetic geometry: elliptic curves and Drinfeld modules, in particular canonical heights, special values of analytic functions, L-series and modular forms.
   http://www.math.tamu.edu/~map/

Parsell, Scott  
   Penn State University. Exponential sums; Hardy-Littlewood method; Diophantine problems. Papers, thesis.
   http://www.math.psu.edu/parsell/

Prasanna, Kartik  
   UCLA. Modular forms. Thesis, teaching information.
   http://www.math.ucla.edu/~kartikp/

Pacelli, Allison M.  
   Williams College. Arithmetic of function fields. Preprints, teaching information.
   http://www.williams.edu/Mathematics/apacelli/

Papaioannou, Thanos  
   Harvard University. Elliptic Curves, Algebraic Geometry, Class Field Theory and Algebraic Topology.
   http://www.people.fas.harvard.edu/~apap/

Petsche, Clayton  
   University of Georgia. Diophantine geometry and arithmetic; Local and global heights on algebraic varieties; Uniform distribution on locally compact groups; Applications of harmonic analysis to number theory; Mahler measure of polynomials. Teaching note
   http://www.math.uga.edu/~clayton/

Pizer, Arnold  
   University of Rochester. Arithmetic of quaternion algebras and its connections to modular forms, Brandt matrices, Hecke operators, and Ramanujan graphs. Pedagogical use of the internet.
   http://www.math.rochester.edu/people/faculty/apizer/

Pollack, David  
   Wesleyan University. Thesis "Explicit Hecke Actions on Modular Forms", Harvard, 1998 (PDF).
   http://www.math.wesleyan.edu/People/faculty_pollack.htm